Toast the pepper in a small saucepan until fragrant, 1 minute. Add the olive oil and heat until bubbles come to the surface. Remove from the heat and let cool completely. (This can be done up to 1 week in advance.)
While the oil is cooling, macerate the shallots in a bowl with the lemon juice, vinegar and 1 teaspoon salt to remove potency. Slowly whisk in the pepper oil until emulsified. Add the Parmesan and pecorino; stir to combine.